Conventionally, when the aircraft receives, during the cruising phase when it is following the cruising level with a fixed cruising speed, a flight instruction prohibiting it from adopting a downward trajectory, the flight management system FMS guides the aircraft on the cruising level by maintaining the cruising speed. When the aircraft is allowed to follow a downward trajectory, the FMS operates in vertical descent trajectory catch-up mode. There are various vertical descent trajectory catch-up modes, including a catch-up mode at minimum thrust with a target speed for catching up in level VCRP and a target speed for catching up in downward trajectory VCRD. When the FMS operates according to this catch-up mode, it sets the thrust of the engines and the control surfaces of the aircraft as follows: when the aircraft is constrained to follow a level, the FMS sets the position of the control surfaces to guide the aircraft to a level and sets the thrust of the engines to its idle level when the speed V of the aircraft is greater than a target rejoining speed in level VCRP, and it adapts the thrust of the engines to keep the speed equal to the target rejoining speed in level VCRP when the speed of the aircraft reaches the target rejoining speed in level VCRP. When the aircraft is allowed to follow a downward trajectory, the FMS sets the thrust of the engines to its idle level and sets the control surfaces so that the aircraft makes up, by accelerating, a target rejoining speed in descent VCRD. In other words, the FMS sets the pitch angle of the aircraft so that it accelerates to a target rejoining speed in descent VCRD then maintains this target speed.
When the aircraft has rejoined the vertical descent trajectory, the FMS returns the speed of the aircraft to the descent speed value so that the aircraft rejoins the descent flight plan.
However, in vertical descent trajectory catch-up mode, the FMS varies the speed of the aircraft over a small speed range around the descent speed. In practice, conventionally, the target rejoining speed in level VCDP, respectively the target rejoining speed in descent VCRD, is equal to the descent speed downrated, respectively uprated, by 20 knots. When the aircraft is constrained to remain for a long time on a level, a very wide excursion of the aircraft above the vertical descent trajectory may be generated. In this case, the piloting of the FMS in catch-up mode does not enable the aircraft to rejoin the descent flight plan early enough before the approach phase to guarantee the success of the approach phase. Quite often, for the aircraft to catch up on the descent flight plan, the pilot is constrained to manually use the air brakes. However, the air brakes are great consumers of energy. This unnecessary consumption results from poor speed management. The air brakes also generate vibrations that are uncomfortable for the passengers. Another solution for rejoining the descent flight plan entails manually piloting the aircraft. This type of piloting presents the drawback of representing a significant workload for the crew which is already stressed in a descent phase.